%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL030-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 00:36:15 EDT 2022
% Result : Unsatisfiable 0.60s 0.78s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 44 ( 43 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ).
cnf(l_definition,axiom,
apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ).
cnf(prove_fixed_point,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
cnf(refute_0_0,plain,
apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) != apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26)))),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(apply(s,X_26),X_26)))]]) ).
cnf(refute_0_1,plain,
apply(apply(l,X),apply(X_7,X_9)) = apply(X,apply(apply(X_7,X_9),apply(X_7,X_9))),
inference(subst,[],[l_definition:[bind(Y,$fot(apply(X_7,X_9)))]]) ).
cnf(refute_0_2,plain,
apply(apply(apply(s,X_7),X_7),X_9) = apply(apply(X_7,X_9),apply(X_7,X_9)),
inference(subst,[],[s_definition:[bind(X,$fot(X_7)),bind(Y,$fot(X_7)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( apply(apply(apply(s,X_7),X_7),X_9) != apply(apply(X_7,X_9),apply(X_7,X_9))
| apply(apply(X_7,X_9),apply(X_7,X_9)) = apply(apply(apply(s,X_7),X_7),X_9) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(apply(s,X_7),X_7),X_9))),bind(Y0,$fot(apply(apply(X_7,X_9),apply(X_7,X_9))))]]) ).
cnf(refute_0_7,plain,
apply(apply(X_7,X_9),apply(X_7,X_9)) = apply(apply(apply(s,X_7),X_7),X_9),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,X_7),X_7),X_9),apply(apply(X_7,X_9),apply(X_7,X_9))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( apply(apply(X_7,X_9),apply(X_7,X_9)) != apply(apply(apply(s,X_7),X_7),X_9)
| apply(apply(l,X),apply(X_7,X_9)) != apply(X,apply(apply(X_7,X_9),apply(X_7,X_9)))
| apply(apply(l,X),apply(X_7,X_9)) = apply(X,apply(apply(apply(s,X_7),X_7),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(l,X),apply(X_7,X_9)),apply(X,apply(apply(X_7,X_9),apply(X_7,X_9)))) ),[1,1],$fot(apply(apply(apply(s,X_7),X_7),X_9))]]) ).
cnf(refute_0_9,plain,
( apply(apply(l,X),apply(X_7,X_9)) != apply(X,apply(apply(X_7,X_9),apply(X_7,X_9)))
| apply(apply(l,X),apply(X_7,X_9)) = apply(X,apply(apply(apply(s,X_7),X_7),X_9)) ),
inference(resolve,[$cnf( $equal(apply(apply(X_7,X_9),apply(X_7,X_9)),apply(apply(apply(s,X_7),X_7),X_9)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
apply(apply(l,X),apply(X_7,X_9)) = apply(X,apply(apply(apply(s,X_7),X_7),X_9)),
inference(resolve,[$cnf( $equal(apply(apply(l,X),apply(X_7,X_9)),apply(X,apply(apply(X_7,X_9),apply(X_7,X_9)))) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))) = apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26)))),
inference(subst,[],[refute_0_10:[bind(X,$fot(f(apply(apply(s,X_26),X_26)))),bind(X_7,$fot(X_26)),bind(X_9,$fot(f(apply(apply(s,X_26),X_26))))]]) ).
cnf(refute_0_12,plain,
( apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))) != apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))))
| apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26)))) = apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))))),bind(Y0,$fot(apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))))))]]) ).
cnf(refute_0_13,plain,
apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26)))) = apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))),
inference(resolve,[$cnf( $equal(apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))),apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) != apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26))))
| apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26)))) != apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26))))
| apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) = apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))),apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))))) ),[1],$fot(apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))))]]) ).
cnf(refute_0_15,plain,
( apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) != apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26))))
| apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) = apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26)))) ),
inference(resolve,[$cnf( $equal(apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26)))),apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26))))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) != apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))),apply(f(apply(apply(s,X_26),X_26)),apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))))) )],[refute_0_15,refute_0_0]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(s,X),Y),Z) != apply(apply(X,Z),apply(Y,Z))
| apply(apply(X,Z),apply(Y,Z)) = apply(apply(apply(s,X),Y),Z) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(apply(s,X),Y),Z))),bind(Y0,$fot(apply(apply(X,Z),apply(Y,Z))))]]) ).
cnf(refute_0_18,plain,
apply(apply(X,Z),apply(Y,Z)) = apply(apply(apply(s,X),Y),Z),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,X),Y),Z),apply(apply(X,Z),apply(Y,Z))) )],[s_definition,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))) = apply(apply(apply(s,l),X_26),f(apply(apply(s,X_26),X_26))),
inference(subst,[],[refute_0_18:[bind(X,$fot(l)),bind(Y,$fot(X_26)),bind(Z,$fot(f(apply(apply(s,X_26),X_26))))]]) ).
cnf(refute_0_20,plain,
( apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) != apply(apply(apply(s,l),X_26),f(apply(apply(s,X_26),X_26)))
| apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))) != apply(apply(apply(s,l),X_26),f(apply(apply(s,X_26),X_26)))
| apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) = apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))),apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26))))) ),[1],$fot(apply(apply(apply(s,l),X_26),f(apply(apply(s,X_26),X_26))))]]) ).
cnf(refute_0_21,plain,
( apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) != apply(apply(apply(s,l),X_26),f(apply(apply(s,X_26),X_26)))
| apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) = apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))) ),
inference(resolve,[$cnf( $equal(apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26)))),apply(apply(apply(s,l),X_26),f(apply(apply(s,X_26),X_26)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))) != apply(apply(apply(s,l),X_26),f(apply(apply(s,X_26),X_26))),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,X_26),X_26),f(apply(apply(s,X_26),X_26))),apply(apply(l,f(apply(apply(s,X_26),X_26))),apply(X_26,f(apply(apply(s,X_26),X_26))))) )],[refute_0_21,refute_0_16]) ).
cnf(refute_0_23,plain,
apply(apply(apply(s,l),l),f(apply(apply(s,l),l))) != apply(apply(apply(s,l),l),f(apply(apply(s,l),l))),
inference(subst,[],[refute_0_22:[bind(X_26,$fot(l))]]) ).
cnf(refute_0_24,plain,
apply(apply(apply(s,l),l),f(apply(apply(s,l),l))) = apply(apply(apply(s,l),l),f(apply(apply(s,l),l))),
introduced(tautology,[refl,[$fot(apply(apply(apply(s,l),l),f(apply(apply(s,l),l))))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(apply(s,l),l),f(apply(apply(s,l),l))),apply(apply(apply(s,l),l),f(apply(apply(s,l),l)))) )],[refute_0_24,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL030-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 09:07:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.78
% 0.60/0.78 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.60/0.79
%------------------------------------------------------------------------------